List of new best solutions found by FICO(R) Xpress Solver, together with verification script output:

--> Problem 8 2D, 16 points:
(0.2799882855914676, 0.5723506487172881), (0.665264317553864, 0.3274156810489232), (0.18869960149956658, 0.1195741691936406), (0.14871008843577532, 0.8602636683287943), (0.6675239812002706, 0.9744362157322729), (0.9271482385872852, 0.23254215848147136), (0.49991419140392523, 0.743279528472159), (0.3900926714528368, 0.9992548137324104), (0.4405236025597568, 0.0005414053757727264), (0.005766195011044914, 0.6212006348232103), (0.7367237374397657, 0.5966324765707136), (0.9986075594952186, 0.501758911908645), (0.7140435924789984, 0.0531807754068185), (0.3869937631220582, 0.315185144161753), (0.9005723697003767, 0.8218828281130218), (0.02260054581879767, 0.3431702379652192)
Construction 1 has 16 points in 2 dimensions.
Ratio of max distance to min distance: sqrt(12.889246742491403)

--> Problem 8 3D, 14 points:
(0.8877293234766775, 0.7781086725343221, 0.2856795900572496), (0.6042472092823249, 0.39016676249570265, 0.9687619853120806), (0.4972978803000714, 0.5008656339341403, 0.5036182713520507), (0.6589245362888685, 0.8495689429977142, 0.8074828911606606), (0.23847076921519142, 0.9528132063754513, 0.5781139343342627), (0.27461698195807116, 0.46945967584201426, 0.027987526761976148), (0.1605647280227378, 0.5819521007614142, 0.88866756150651), (0.8055726769891788, 0.30786912055986726, 0.17533504224988244), (0.39452188683742523, 0.05523384578423523, 0.2605614753058619), (0.9838120810304894, 0.5052801955925672, 0.6811332517940586), (0.442966699408178, 0.9171247155501066, 0.13431372991230683), (0.014804108637984068, 0.44163455310882244, 0.4424437209572573), (0.738713928927795, 0.08743583947230994, 0.607758441179669), (0.265553057854492, 0.1315029766035893, 0.7270386174709309)
Construction 2 has 14 points in 3 dimensions.
Ratio of max distance to min distance: sqrt(4.165783988278149)

--> Problem 12, 26 circles
(0.8965111839, 0.5181889362, 0.1034888147), (0.2962816128, 0.867633318, 0.1323666633), (0.2983096164, 0.6192772801, 0.115996955), (0.7037183599, 0.8676332875, 0.1323666874), (0.7016903579, 0.6192773201, 0.1159969811), (0.1051017935, 0.7267732975, 0.105101792), (0.8891949913, 0.1108050127, 0.1108050075), (0.686603769, 0.09260232215, 0.09260231943), (0.4040343928, 0.257958252, 0.09596559425), (0.3133962114, 0.09260232032, 0.09260231754), (0.7603250013, 0.237195673, 0.0697000406), (0.4999999612, 0.7294239379, 0.113810096), (0.9153829641, 0.9153829631, 0.08461703442), (0.4999999779, 0.9216170191, 0.07838297891), (0.727242311, 0.4042219542, 0.1005710381), (0.4999999854, 0.4687694851, 0.1356607495), (0.9041877857, 0.3190357969, 0.09581221317), (0.1034888103, 0.5181889273, 0.103488809), (0.4999999892, 0.09400674753, 0.09400674394), (0.5959655829, 0.2579582541, 0.09596559474), (0.09581220515, 0.3190358029, 0.09581220403), (0.272757669, 0.4042219464, 0.1005710314), (0.2396749742, 0.2371956682, 0.06970004157), (0.8948982185, 0.7267732996, 0.10510178), (0.08461703175, 0.9153829672, 0.08461703024), (0.1108049995, 0.1108050035, 0.1108049983)
Construction 1 has 26 circles.
The circles are disjoint and lie inside the unit square.
Construction 1 sum of radii: 2.6359155161400003

--> Problem 13, 21 circles
(0.6785278724095114, 0.7313385918570083, 0.08641206324529), (0.3628414047203541, 0.11508312623483812, 0.11508312623483), (0.6785278724095123, 0.291930304612819, 0.08641206324529), (0.8396598064136079, 0.8861975993532661, 0.13707129711656), (0.07474150007182763, 0.3164721426564959, 0.07474150007182), (0.07474150007182474, 0.706796753813332, 0.07474150007182), (0.1274001909316823, 0.5116344482349167, 0.12740019093168), (0.3724426188909824, 0.511634448234916, 0.11764223702743), (0.8576682471862885, 0.3925715918910206, 0.11906285634388), (0.1239616077379894, 0.8993072887318397, 0.12396160773798), (0.4808315218485262, 0.3091443395002152, 0.11203231188848), (0.12396160773798695, 0.12396160773798698, 0.12396160773798), (0.8576682471862881, 0.630697304578806, 0.11906285634388), (0.36284140472035875, 0.9081857702349935, 0.11508312623483), (0.2591686357665864, 0.708742625654103, 0.1096959006846), (0.6289100808115198, 0.5116344482349142, 0.13882522489274), (0.5908359840356403, 0.11292169820595797, 0.11292169820595), (0.8396598064136092, 0.1370712971165618, 0.13707129711656), (0.4808315218485263, 0.7141245569696164, 0.11203231188848), (0.5908359840356409, 0.9103471982638728, 0.11292169820595), (0.2591686357665813, 0.31452627081572604, 0.10969590068461)
Construction has 21 disjoint circles.
Perimeter of minimum circumscribing rectangle: 4.000000
Sum of radii: 2.36583237591064